## Understanding the (x-y)(x^2 + xy + y^2) Formula

The formula (x-y)(x^2 + xy + y^2) is a special case of a more general algebraic concept known as **the difference of cubes**. It provides a quick and efficient way to factor expressions that fit a specific pattern.

### The Difference of Cubes Formula

The general formula for the difference of cubes is:

**a³ - b³ = (a - b)(a² + ab + b²)**

This formula states that the difference of two cubes can be factored into the product of the difference of their cube roots and a quadratic expression.

### Applying the Formula to (x-y)(x^2 + xy + y^2)

In our specific case, we can see that:

**a = x****b = y**

Therefore, applying the difference of cubes formula, we get:

**(x³ - y³) = (x - y)(x² + xy + y²)**

### How to Use the Formula

The formula is useful for:

**Factoring expressions:**If you encounter an expression in the form a³ - b³, you can immediately factor it using the formula.**Simplifying expressions:**By factoring, you can often simplify complex expressions, making them easier to work with.**Solving equations:**The formula can be used to solve equations involving the difference of cubes.

### Example

**Factor the expression x³ - 8**

- Recognize that 8 is the cube of 2 (2³ = 8).
- Apply the difference of cubes formula:
- a = x
- b = 2

- (x³ - 2³) = (x - 2)(x² + 2x + 4)

Therefore, the factored form of x³ - 8 is **(x - 2)(x² + 2x + 4)**.

### Conclusion

The (x-y)(x² + xy + y²) formula, derived from the difference of cubes formula, provides a valuable tool for factoring and simplifying expressions. Understanding this formula can save you time and effort when working with algebraic expressions.